AMC states and AME states are potential maximally coherent states and maximally entangled states, since they can be decomposed as the convex combinations of maximally coherent and maximally entangled pure states, respectively. Furthermore, they can be collapsed to maximally coherent states and maximally entangled states with the help of another party's local measurements and classical communication operationally, if only one knows the optimal pure state decompositions. As applications, one can transform the AMC states to maximally coherent pure states with the help of another party's local measurements and classical communication for the purpose of quantum information processing such as the Deutsch-Jozsa algorithm to speedup the computation [1]}. In this sense, the AMC states are potentially perfect quantum resources. In fact, the experimental realization in linear optical systems for obtaining the coherence of assistance with respect to the relative entropy coherence in two dimensional systems has already been presented [2]}.
